The Topological Properties of the Non-Hermitian Su–Schrieffer–Heeger Model Incorporating Long-Range Hopping and Spin–Orbit Coupling

Long-range hopping plays a crucial regulatory role in non-Hermitian topological systems. This paper systematically studies a non-Hermitian Su–Schrieffer–Heeger (SSH) model that incorporates both long-range hopping and spin–orbit coupling (SOC) within the framework of the generalized Brillouin zone (GBZ). We reveal that long-range hopping can not only actively suppress the non-Hermitian skin effect, but can also cooperate with SOC to jointly modulate the stability regions of topological phases. SOC controls topological transitions through real or imaginary coupling properties and enhances the robustness of edge states. By constructing the GBZ and establishing the non-Bloch bulk–boundary correspondence, we demonstrate that the topological zero modes are entirely determined by the non-Bloch winding number. This study clarifies the key role of long-range hopping as a core regulatory parameter and provides a new paradigm for achieving the synergistic control of topological states and localized properties in non-Hermitian systems through designed couplings.